The Frobenius formalism in Galois quantum systems

Details The Frobenius formalism in Galois quantum systems The Frobenius formalism in Galois quantum systems

2006-05-05

arxiv.org/abs/quant-ph/0605054v1

Acta Applicandae Mathematicae 93 (2006) 197-214

Physics

Quantum Physics

Scientific paper

10.1007/s10440-006-9040-7

Quantum systems in which the position and momentum take values in the ring ${\cal Z}_d$ and which are described with $d$-dimensional Hilbert space, are considered. When $d$ is the power of a prime, the position and momentum take values in the Galois field $GF(p^ \ell)$, the position-momentum phase space is a finite geometry and the corresponding `Galois quantum systems' have stronger properties. The study of these systems uses ideas from the subject of field extension in the context of quantum mechanics. The Frobenius automorphism in Galois fields leads to Frobenius subspaces and Frobenius transformations in Galois quantum systems. Links between the Frobenius formalism and Riemann surfaces, are discussed.

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